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**Mixtures And Alligation** is an integral topic in the Quantitative section of all employment and admission tests. There are a lot of questions asked every year from this topic and thus, is very crucial from the examination point of view. So, here is an explanation of the Mixture and Alligation along with various illustrations to help the candidates learn the topic with ease.

**Alligation:**Rule of alligation enables us to find the ratio in which two or more ingredients at a given price must be mixed to produce a resultant mixture of the desired price.**Mean Price:**It is the cost of unit quantity of a mixture.-
**Mixture:**Mixture is formed by mixing two or more quantities. It can be expressed in the form of percentage or ratio.

10 % of sugar in water

A solution of water and sugar is 12 : 20, which means water : sugar = 12 : 20

According to the rule of alligation: When two ingredients are mixed,

If a vessel contains A liters of milk and if B litres of milk is withdrawn and replaced by water, and again if B litres of mixture is withdrawn and replaced by water and this operation is replaced n times in all, then

Simplified formula to calculate quantity of milk left after n^{th}operation = [A(1 – (B/A))^{n}]

When two or more different ingredients are mixed together, a simple mixture is formed.

When two or more simple mixtures are mixed together, a compound mixture is formed.

## 1) Rule of alligation:## Points to Remember While Using the Rule of Alligation- The three values alligated should always represent the same variable and should have same units.
- alligation of 3 values of cost gives the ratio in terms of number and vice-versa.
- If two values of cost price and selling price of the mixture are given, then in such cases first calculate the cost price of the mixture and then allegate the 3 values of cost price.
- A and B represent concentration if the numerical is based on mixing of solutions.
## Applications Of MixturesConsider the following common data to understand the application better. A= 20 B=10 Na =30 Nb= 45 The answer will be 14, in each of the following cases. ## Average of a class## ExampleClass A has 30 students scoring average marks of 20 and Class B has 45 students scoring average marks of 10.What is the average of both classes together (14). ## Average price of goods## ExampleSunita buys 30 kgs of sugar at Rs 20/kg and 45 kgs of sugar at 10/kg. What is the average price? (Rs 14/kg). ## Percentage## ExampleAn antique article salesman makes a profit of 20% by selling 30% of his articles and a profit of 10% by selling 45% of his goods.
What is his net percentage profit? (14%). ## Average Speed## ExampleA bus travels at 20kmph for 30 km and at 10 kmph for 45 km. Find the average speed of the bus for the entire journey (14kmph). ## Mixtures## ExampleA dishonest milkman dilutes two milk cans such that milk can A containing 30 liters is mixed with 20% water and milk can B containing 45 liters is mixed with 10% water. He combines both mixtures. Find the percentage of water in the final mixture (14%). |

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